Presentació feta a la XXVIII Reunió Anual XRQTC celebrada a la Facultat de Biologia de la Universitat de Barcelona els dies 11 i 12 de juny de 2012.

2. From all-metal aromatic clusters to
open-shell spherical aromaticity
Jordi Poater
Institut de QuímicaComputacional
and Departament de Química,
Universitat de Girona

3. Fullerenes
1985
• The concept of
aromaticityis no Nanotubes 1991
longer confined to
"carbon chemistry"
but can be applied 2001 All-metal Aromaticity
to the entire
periodic table. d-orbital Aromaticity
2005
2007 -Aromaticity
f-orbital Aromaticity 2008

4. Open-shellsphericalaromaticity
• Hückel’s 4n+2 rule
coronene pyrene
Dnh
n
Aromaticityof (4n+2)p-annuleneswithDnhsymmetry comes fromthefulfillmentof a
closed-shellthatprovides extra stability.

5. Open-shellsphericalaromaticity
• Baird’s 4n rule
Dnh
n
Aromaticityoflowest-lyingtripletstateof(4n)p-annuleneswithDnhsymmetry comes
fromthesame-spinhalf-filleddegeneratehighest-occupiedMOsthatprovides extra
stability.

6. Open-shellsphericalaromaticity
• Hirsch’s 2(n+1)2ruleforsphericalaromaticity
Rotor rigid solution
n=3 32
n=2 18
n=1 8
n=0 2
2, 8, 18, 32, 50, 72, 98… = 2(n+1)2
A. Hirsch, Z. Chen and H. Jiao, Angew. Chem. Int. Ed. 2000, 39, 3915

7. Open-shellsphericalaromaticity
• Hirsch’s
2(n+1)2ruleforsphericalaromatici
ty
Z. Cheng and R. B. Bruce Chem. Rev.,2005, 105, 3613

8. Open-shellsphericalaromaticity
PLANAR SPHERICAL
CLOSED-SHELL 4n+2 Hückel’s rule 2(n+1)2 Hirsch’s rule
4n lowest-lying
OPEN-SHELL triplet excited state ?
Baird’s rule

9. Open-shellsphericalaromaticity
• 2n2+2n+1 (S=n+1/2) rulefor open-shellsphericalaromaticity
n=3 32
n=2 18
n=1 8
n=0 2
1, 5, 13, 25, 41, 61, 75… = 2n2+2n+1; (S=n+1/2)
J. Poater and M. Solà Chem. Commun. 2011, 47, 11647

10. Open-shellsphericalaromaticity
• Aromaticityindices
Magnetic shielding tensor
Multicenter delocalization indices
A = {A1, A2, …, AN}
For monodeterminantal WFs: I ring ( A )  n i1  niN S i1i2 A1 S i2i3 A2  S iN i1 AN 
i1 ,i2 ,,i N
M. Giambiagi, M. S. de Giambiagi, C. D. dos Santos Silva and A. P. de Figuereido,Phys. Chem. Chem. Phys. 2000, 2, 3381
1
MCI ( A ) 
2N
I
P( A )
ring ( A)
P. Bultinck, R. Ponec and S. van Damme,J. Phys. Org. Chem. 2005, 18, 706

11. Open-shellsphericalaromaticity
Systems symm. NICS(1)zz MCI r(C,C) Spin
C202+ Ih -7.4 0.020 1.447 S=0
C207+ Ih -4.0 0.035 1.494 S = 3/2
C205- Ih -18.0 0.024 1.508 S = 7/2
J. Poater and M. Solà Chem. Commun. 2011, 47, 11647

12. Open-shellsphericalaromaticity
Systems symm Ring NICS(1)zz MCI BLA Spin
C60 Ih 6-MR 0.8 0.018 0.058 S=0
5-MR 21.5 0.011
C601- Ih 6-MR -1.4 0.017 0.002 S = 11/2
5-MR -19.9 0.049
C6019+ Ih 6-MR -14.9 0.019 0.013 S = 9/2
5-MR -25.3 0.041
C6010+ Ih 6-MR -18.6 0.011 0.030 S=0
5-MR -29.5 0.017
J. Poater and M. Solà Chem. Commun. 2011, 47, 11647

13. Open-shellsphericalaromaticity
Systems symm. Ring NICS(1)zz MCI BLA Spin
C80 S6 5-MR 10.7 0.019 S=0
6-MR -5.2 0.012 0.025
5-MR 26.3 0.018
6-MR 11.3 0.014 0.001
6-MR -5.1 0.012 0.025
C808+ Ih 6-MR -7.2 0.011 0.015 S=0
5-MR -4.0 0.017
C805- Ih 6-MR -20.8 0.019 0.012 S = 13/2
5-MR -5.5 0.034
J. Poater and M. Solà Chem. Commun. 2011, 47, 11647

14. Open-shellsphericalaromaticity
Systems symm. NICS(1)zz MCI Spin
Ge122- Ih -5.5 0.049 S=0
Ge121- Ih -405.9 0.113 S = 5/2
Ge124+ Ih -69.0 0.088 S=0

15. All-metal aromatic clusters
• All-metal and semimetal aromatic clusters
are among the most exciting molecules
synthesized since the beginning of the present
century.
• These compounds can have not only the
conventional p-(anti)aromaticity of classical
organic compounds, but also - or even - and
-(anti)aromaticity, thus giving rise to the so-
called multifold aromaticity.

16. All-metal aromatic clusters
• Thetendencyofp-electrons in
classicalorganicaromaticmoleculesisalwaystolocalizethedoublebond
s (distortivecharacter), againstthedelocalizingforceofthe-electrons.
S.C.A.H. Pierrefixe, F.M. Bickelhaupt, Chem. Eur. J. 2007, 13, 6321
• Thus, whilemany of thepropertiesattributedtoaromaticity derive
fromthep-electrons, the-electrons are
theonesresponsibleforthesymmetricframework of
monocyclicaromaticcompounds.

17. All-metal aromatic clusters
• Al42-wasthefirstall-metal compoundssynthesized, containinga pair of
delocalized p-electrons (orbital 1a2u) and two pairs of -electrons (orbitals
1b2g and 2a1g) that contribute to the overall aromaticity of this species.
X. Li, A.E. Kuznetsov, H.F. Zhang, A.I. Boldyrev, L.S. Wang, Science 2001, 291, 859.
• Thus, Al42- can be considered as a “3-
fold” aromatic system ( + paromatic)

18. All-metal aromatic clusters
• Are the p-electrons of the Al42- cluster
distortive, i.e., do they work against the
regular "aromatic" structure with
delocalized, equivalent bonds? Or is this
propensity a characteristic of only classical
aromatic organic molecules?
J. Poater, F. Feixas, F.M. Bickelhaupt and M. Solà Chem. Commun. 2011, 47, 11647

19. All-metal aromatic clusters
• AmsterdamDensityFunctional
• BP86/TZ2P, QUILD
• EnergyDecompositionAnalysis
∆E : M2- (aaa) + M2- (bbb) M42-
∆E =∆Eprep + ∆Eint
∆Eint = ∆Velstat + ∆EPauli + ∆Eoi
∆Eoi = SG ∆EG
∆Eint = ∆Velstat + “total ” + “total p”
J. Poater, F. Feixas, F.M. Bickelhaupt and M. Solà Chem. Commun. 2011, 47, 11647

20. All-metal aromatic
clusters
J. Poater, F. Feixas, F.M. Bickelhaupt and M. Solà Chem. Commun. 2011, 47, 11647

21. All-metal aromatic
clusters
50
40
30 total 
20
DEint
10
0
total p
90 92 94 96 98 100
-10
DVelstat
-20
-30
•Equivalenttrendstothosefound in
benzene.
J. Poater, F. Feixas, F.M. Bickelhaupt and M. Solà Chem. Commun. 2011, 47, 11647

22. NICS(1b2g)= +10.8ppm
NICS(2a1g)=-3.9ppm

26. ACKNOWLEDGMENTS
Prof. Dr. MiquelSolà(UdG) Prof. Dr. F. Matthias Bickelhaupt
Dr. FerranFeixas (San Diego, USA)

27. http://iqc.udg.edu
19/4/2012 Toulouse RECENT ADVANCES IN AROMATICITY 27